2-D Inverse Discrete Cosine Transform

Consider the result obtained after DCT. (Check 2d-DCT )

Apply Inverse Discrete Cosine Transform to obtain the original Image.

MATLAB CODE:

%2-D INVERSE DISCRETE COSINE TRANSFORM

%PREALLOCATE THE MATRIX

A=zeros(size(B));

Temp=zeros(size(B));

[M N]=size(B);

x=1:M;

x=repmat(x',1,N);

y=repmat(1:N,M,1);

figure,

imshow(log(abs(B)),[]);colormap(jet);title('After DCT');

for i=1:M

    for j = 1: N

   

        if(i==1)

          AlphaP=sqrt(1/M);

        else

          AlphaP=sqrt(2/M);

        end

       

        if(j==1)

          AlphaQ=sqrt(1/N);

        else

          AlphaQ=sqrt(2/N);

        end

                 

        cs1=cos((pi*(2*x-1)*(i-1))/(2*M));

        cs2=cos((pi*(2*y-1)*(j-1))/(2*N));

        Temp=B.*cs1.*cs2*AlphaP*AlphaQ;

              

          A(i,j)=sum(sum(Temp));

    end

end

%OUTPUT

figure,

imshow(abs(A),[0 255]);title('Image after IDCT');